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<div><a href="../../index.html">Home</a> &gt;  <a href="../index.html">CO4OI</a> &gt; <a href="index.html">misc</a> &gt; soft_sgv.m</div>

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<h1>soft_sgv
</h1>

<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
<div class="box"><strong>soft_sgv computes the singular value soft-threasholding and PSD</strong></div>

<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
<div class="box"><strong>function [p,r]=soft_sgv(z, N, lambda) </strong></div>

<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
<div class="fragment"><pre class="comment"> soft_sgv computes the singular value soft-threasholding and PSD
 projection

   INPUTS
   
   - N: dimension of the squared matrix
   - z: matrix (unfolded)
   - lambda: soft-thresholding parameter

   OUTPUTS
   
   - p: low-rank approximation of the matrix (unfolded)
   - r: rank of the low-rank approximation matrix</pre></div>

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<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
This function calls:
<ul style="list-style-image:url(../../matlabicon.gif)">
</ul>
This function is called by:
<ul style="list-style-image:url(../../matlabicon.gif)">
</ul>
<!-- crossreference -->



<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
<div class="fragment"><pre>0001 <a name="_sub0" href="#_subfunctions" class="code">function [p,r]=soft_sgv(z, N, lambda)</a>
0002 <span class="comment">% soft_sgv computes the singular value soft-threasholding and PSD</span>
0003 <span class="comment">% projection</span>
0004 <span class="comment">%</span>
0005 <span class="comment">%   INPUTS</span>
0006 <span class="comment">%</span>
0007 <span class="comment">%   - N: dimension of the squared matrix</span>
0008 <span class="comment">%   - z: matrix (unfolded)</span>
0009 <span class="comment">%   - lambda: soft-thresholding parameter</span>
0010 <span class="comment">%</span>
0011 <span class="comment">%   OUTPUTS</span>
0012 <span class="comment">%</span>
0013 <span class="comment">%   - p: low-rank approximation of the matrix (unfolded)</span>
0014 <span class="comment">%   - r: rank of the low-rank approximation matrix</span>
0015 <span class="comment">%</span>
0016 
0017 <span class="comment">%reshape in matrix form</span>
0018 z = reshape(z, [], N);
0019 
0020 <span class="comment">% symmetrization for rounding errors</span>
0021 z=(z+z.')/2;
0022 
0023 [V,Sigma] = eig(z);
0024 aux=diag(Sigma);
0025 
0026 
0027 <span class="comment">% soft-thresholding</span>
0028 aux=max(aux-lambda,0);
0029 <span class="comment">% PSD projection</span>
0030 aux(aux&lt;0)=0;
0031 <span class="comment">% rank</span>
0032 r=length(find(aux~=0));
0033 
0034 
0035 <span class="comment">%build low-rank approximation</span>
0036 Sigma=diag(aux);
0037 p = V * Sigma * V';
0038 
0039 <span class="comment">%unfold solution</span>
0040 p = p(:);
0041 <span class="keyword">end</span>
0042</pre></div>
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